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![[Identifying Distributions]](_images/icon-distribution.svg "Identifying Distributions")
Identifying Distributions
This web page gives you practice in identifying distributions and their parameters. It is extremely important for you to be able to do this. It shows an understanding of the distributions covered in the course.
Purpose
Welcome to the page that helps you identify distributions and parameters. Below, you will find a graphic of a distribution. Your job is to determine the following about that distribution:
- the type of distribution (discrete or continuous)
- the name of the distribution
- the number of parameters it has
- the name of those parameters
- the values of those parameters
Distribution Graphic
Answers
Hover over the grey boxes to see the correct answer.
| Distribution Type | Continuous | |
| Distribution Name | Normal | |
| Number of Parameters | 2 | |
| Parameter Name(s) | μ (mean) σ (standard deviation) | |
| Parameter Value(s) | μ (mean) = -2 σ (standard deviation) = 2 |
Explanation
The sample space an interval. That means this is a continuous distribution. The sample space is not bounded. That means this is a Normal distribution. The other two continuous distributions are either bounded on both sides (Uniform) or bounded below (Exponential).
The Normal distribution has two parameters: μ (mean) and σ (standard deviation). Only the first is obvious from the graphic: μ ≈ -2.
The second parameter, σ, is the standard deviation. Recall from the empirical rule that approximately 68% of the data are within one standard deviation of the mean. So, you could estimate the middle 68% of the data and determine σ from that.
A second option is to find the points of inflection. They are located at μ − σ and μ + σ. A point of inflection is where the curve changes from concave-down to concave-up (or vice-versa). From the graphic, it appears as though the points of inflection are approximately -4 and 0. Thus, the value of σ is approximately 2.
Another Example
Let’s try another example. Click “Refresh” in your browser to get another graphic.